This type of measurement is used in many fields of measuring technology and is a particularly useful technique for optical measuring. The actual measuring signal is superimposed on a carrier wave so that the measurement is expressed by a modulation of the frequency or phase of the combined signal. In phase-measuring technology, the signal is measured along a plurality of different phase steps defined by preselected phase angles of the carrier wave. For instance, the simplest known formula for such evaluation results when three measured values, at phase angles .pi./4, 3.pi./4, and 5.pi./4 relative to the carrier wave, are recorded.
Due to the effect of the phase modulation, the combined signal is actually measured at slightly different phase angles, that is, the phase angles relative to the combined signal do not exactly correspond to the desired phase angles relative to the carrier wave. As a result, erroneous phase values of the modulation signal are measured systematically. Therefore, the results achieved with this type of method are adequately accurate only when the frequency of the modulation signal is considerably lower than the frequency of the carrier wave.
Phase-measuring techniques are often used in optical-measuring technology for the evaluation of bar pattern images. For example, U.S. Pat. No. 4,744,659 to Kitabayashi discloses an interferometer where the reference and measuring beams interfere at predetermined angles of inclination relative to a detector surface. As a result of this inclination of the two beams, a bar pattern representing a spatial carrier wave is generated on the detector surface. The frequency of this carrier wave is determined by the angle of inclination. Deviations of the surface profile of the measured surface from the surface profile of the reference mirror result in a spatial modulation of the bar image, that is, the phase angle of the bar image deviates locally from the phase angle of the carrier wave by an amount which is determined by the angle of inclination. The intensity distribution of the bar pattern is measured and, as a result of two Fourier transformations of the intensity distribution, the deviation of the phase angle of the bar pattern from the carrier wave is computed. By means of a window function, a sideband of the spatial frequency spectrum is filtered out.
However, the two Fourier transformations require such a significant amount of computation time that an evaluation of the interferograms in video real time is not possible. In addition, filtering out the sideband has the effect of a low-pass filter, thereby changing the measured value.
An alternative method for evaluating multiple-bar interferograms by Fourier transformation has been disclosed in Optical Engineering, Vol. 23, No. 4, page 391 (1984), where the measured intensity distribution of the bar pattern is first multiplied by a function of the frequency of the carrier wave, and then a convolution of the product is performed with a window function. This window function is selected in such a way that--for calculating the phase value in one point of the interferogram--the interferogram intensities of a spatial region covering several periods of the carrier wave are used. However, also with this method, the convolution of the measured intensity values over several periods of the carrier wave has the effect of a low-pass filter, resulting in a reduction of spatial resolution. Further, this prior art method does not provide an analysis of errors occurring in the computation of phase values, particularly when the bar frequency deviates from the carrier frequency.
Therefore, known phase-measuring technology is burdened by the above-mentioned systemic errors, and the methods for evaluation of multiple-bar interferograms provide correct phase values principally only when the bar frequency of the bar pattern corresponds to the bar frequency determined by the angle of inclination, that is, when the profile of the measured surface corresponds fairly closely to the profile of the reference surface. Further, since this method measures the deviations of both profiles, the values relating to the sample being measured exhibit this systemic error.
Another known phase-measuring technique, sometimes referred to as phase-shift interferometry, has been described in Applied Optics, Vol. 22, No. 21, page 3421 (1983). According to this method, several interferograms are recorded at time intervals without a spatial carrier wave. Instead, a time carrier wave is generated in that, between the recording of each interferogram, the reference mirror is shifted parallel to the optical axis (n-1) times by the same distance .lambda./2n, where .lambda. is the wavelength of the light in the interferometer. This results in a phase shift of 2.pi./n, where n is the number of interferograms. By using at least four interferograms, identical points on each of the interferograms can be used to calculate a phase value .phi.=arc tangent (Z/N), where Z and N (relating, respectively, to the sine and cosine functions of the phase value) are computed from the intensities of the respective interferograms.
The accuracy attainable with this just-described phase-shift method is essentially a function of the accuracy with which the reference mirror is shifted relative to the intended position. Therefore, high-quality expensive piezo translators are used for shifting.
An analysis of the error in phase value, as a function of the phase shift which has in fact occurred, shows that, in the case of the intended phase shift, the error has a value of zero; and in the case of any deviation from the intended phase shift, the error increases quantitatively in a linear direction. The last-cited reference suggests that the measuring procedure be carried out twice in sequence. Between the two passes, the phase is shifted again by .pi./2. If, after the first pass, the phase value is computed based on the equation tan(.phi..sub.1)=Z.sub.1 /N.sub.1 and, after the second pass, based on the equation tan(.phi.2) =Z.sub.2 /N.sub.2, an improved phase value tan (.phi.)=(Z.sub.1 +Z.sub.2)/(N.sub.1 +N.sub.2) is obtained.
The present invention is a method of the above-described type in which systemic measuring errors are significantly reduced.